testing the flavour sector of susy models @ lhcific.uv.es/~flasy2011/porod.pdf · Φtp2 testing...
TRANSCRIPT
ΦTP2
Testing the flavour sector of
SUSY models LHC
Werner Porod
Universitat Wurzburg
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 1
ΦTP2Overview
Flavour Generalities
LFV signals in models with
Dirac neutrinos
Majorana neutrinos
General MSSM + extensions
Squark flavour at LHC
Conclusions
More in F del Aguila et al EPJC 57 (2008) 183 [arXiv08011800]
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 2
ΦTP2Supersymmetry MSSM
Standard Model MSSM
mattere d d d
νe u u uhArr
e d d d
νe u u u
gauge sector hArrγ Z0 Wplusmn g γ z0 wplusmn g
Higgs sector hArrH0 h0hArrh0 H0 A0 Hplusmn h0d h0
u hplusmn
assume conserved R-Parity (minus1)(3(BminusL)+2s)
(γ z0 h0d h
0u) rarr χ0
i (wplusmn hplusmn) rarr χplusmnj
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 3
ΦTP2Flavour Generalities
SM Higgs doublet + Yukawa couplings
rArr after EWSB CKM- and PMNS matrices
rArr excellent agreement with data eg
BR(brarr sγ) BR(B+u rarr τ+ν) BR(Bs rarr micro+microminus) BR(B rarr Dτν)
BR(brarr smicro+microminus) BR(Bd rarr micro+microminus) BR(Bd rarr micro+microminus) ∆MBs ∆MBd
BR(Ds rarr τν) BR(Ds rarr microν) ∆MD
BR(K rarr microν) BR(K0L rarr π0νν) BR(K+ rarr π+νν) ∆mK ǫK
BR(τ rarr eγ) BR(τ rarr microγ) BR(τ rarr lllprime) (l lprime = e micro)
BR(microrarr eγ) BR(microminus rarr eminuse+eminus)
electric dipolemoments eg dn de
However no clue what determines sizes of masses and mixing angles
Supersymmetry eg MSSM
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus microHdHu
Vsoft = HdLTeelowast +HdQTdd
lowast +HuQTuulowast
+X
f=LeQdu
flowastM2ff +M2
Hd|Hu|2 +M2
Hu|Hu|2 minusBmicroHdHu
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 4
ΦTP2Flavour Generalities
Pragmatic approach Minimal Flavour Violationdagger
express all additional flavour structures in terms of rsquoknownrsquo Yukawas
eg at some (high) scale
Tf = A0fYf M2f
= M20f13 + αY dagger
f Yf
where A0f and M20f are scalars
generic prediction for squarkslowast FV decays are governed by |VCKMij |2 eg
BR(trarr χ+1 s) ≃ |VCKMts|2BR(trarr χ+
1 s)
BR(trarr χ012c) ltsim 10minus7
Sleptons depend on mechanism for neutrino masses
dagger AJ Buras et al PLB 500 (2001) 161 G DrsquoAmbrosio et al NPB 645 (2002) 155lowast E Lunghi WP O Vives PRD 74 (2006) 075003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 5
ΦTP2Flavour Generalities
more ambitious new symmetries eg Abelian or non-Abelian gauge or discrete
SU(3) flavour examplelowast
WY = Hψiψcj
h
θi3θ
j3 + θi
23θj23
ldquo
θ3θ3rdquo
+ ǫiklθ23kθ3lθj23
ldquo
θ23θ3rdquo
+ i
Yd prop
0
B
B
0 xd12 ε
3 xd13 ε
3
xd12 ε
3 ε2 xd23 ε
2
xd13 ε
3 xd23 ε
2 1
1
C
C
A
Yu prop
0
B
B
0 xu12 ε
3 xu13 ε
3
xu12 ε
3 ε2 xu23 ε
2
xu13 ε
3 xu23 ε
2 1
1
C
C
A
(M2f)ji = m2
0
bdquo
δji
+1
M2f
raquo
θdagger3iθj3 + θ3iθ
dagger3
j+ θdagger23i
θj23 + θ23iθ
dagger23
j+ θdagger123i
θj123 + θ123iθ
dagger123
jndash
+1
M4f
(ǫiklθdagger3
kθdagger23
l)(ǫjmnθ3mθ23n) +
laquo
LHC similar to MFV approach although somewhat larger effects
lowast GG Ross L Velasco-Sevilla O Vives NPB 692 50 (2004) L Calibbi J Jones-Perez
O Vives PRD 78 (2008) 075007 L Calibbi et al NPB 831 (2010) 26
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 6
ΦTP2Lepton flavour violation experimental data
Neutrinos tiny masses
∆m2atm ≃ 3 middot 10minus3 eV2
∆m2sol ≃ 7 middot 10minus5 eV2
3H decay mν ltsim 2 eV
Neutrinos large mixings
| tan θatm|2 ≃ 1
| tan θsol|2 ≃ 04
|Ue3|2 ltsim 005
strong bounds for charged leptons
BR(microrarr eγ) ltsim 12 middot 10minus11 BR(microminus rarr eminuse+eminus) ltsim 10minus12
BR(τ rarr eγ) ltsim 11 middot 10minus7 BR(τ rarr microγ) ltsim 68 middot 10minus8
BR(τ rarr lllprime) ltsim O(10minus8) (l lprime = e micro)
|de| ltsim 10minus27 e cm |dmicro| ltsim 15 middot 10minus18 e cm |dτ | ltsim 15 middot 10minus16 e cm
SUSY contributions to anomalous magnetic moments
|∆ae| le 10minus12 0 le ∆amicro le 43 middot 10minus10 |∆aτ | le 0058
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 7
ΦTP2Dirac neutrinos MFV scenario
analog to leptons or quarks
Yν H νL νR rarr Yν v νL νR = mν νL νR
requires Yν ≪ Ye
rArr no impact for future collider experiments
Exception νR is LSP and thus a candidate for dark matter
rArr long lived NLSP eg t1 rarr l+bνR
Remark mνRhardly runs rArr eg mνR
≃ m0 in mSUGRA
mνR ≃ 0 in GMSB
S Gopalakrishna A de Gouvea and W P JCAP 0605 (2006) 005 JHEP 0611 (2006) 050
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 8
ΦTP2Dirac neutrinos NLSP life times
m (GeV)12
βtan = 10
tan =30β
Lif
e t
ime (
seco
nd
s)
10
800 1000 1200 1400
100
600
1
τ1
m0 = 100 GeV
A0 = 100 GeV
sgn(micro) = 1
m (GeV)ν~1
t~
1
t~
1
m =300 GeV
t~
1
m =250 GeV
m =350 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
m (GeV)t~1
ν~
1
ν~
1
m =200 GeV
ν~
1
m =100 GeV
m =300 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
general signature two long lived particles + multi jets andor multi lepton
S K Gupta B Mukhopadhyaya S K Rai PRD 75 (2007) 075007
D Choudhury S K Gupta B Mukhopadhyaya PRD 78 (2008) 015023
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 9
ΦTP2Majorana neutrinos Seesaw mechanismlowast
Neutrino masses due tof
Λ(HL)(HL)
lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)
M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315
RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich
Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181
(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)
R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 10
ΦTP2The Setup GUT scale
Relevant SU(5) invariant parts of the superpotentials at MGUT
Type-I
WRHN = YIN Nc 5M middot 5H +
1
2MR NcNc
Type-II
W15H =1radic2Y
IIN 5M middot 15 middot 5M +
1radic2λ15H middot 15 middot 5H +
1radic2λ25H middot 15 middot 5H
+M1515 middot 15
Type-III
W24H = 5H24MY IIIN 5M +
1
224MM2424M
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 11
ΦTP2The SU(5)-broken phase
Under SU(3) times SUL(2) times U(1)Y
The 5 10 and 5H contain
5M = ( bDc bL) 10 = (bUc bEc bQ) 5H = ( bHc bHu) 5H = ( bHc bHd)
The 15 decomposes as
15 =bS(6 1minus2
3) + bT (1 3 1) + bZ(3 2
1
6)
The 24 decomposes as
24M =cWM (1 3 0) + bBM (1 1 0) + bXM (3 2minus5
6)
+ bXM (3 25
6) + bGM (8 1 0)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 12
ΦTP2Seesaw I
Postulate very heavy right-handed neutrinos yielding the following superpotential below
MGUT
WI =WMSSM +Wν
Wν = bNcYνbL middot bHu +
1
2bNcMR
bNc
Neutrino mass matrix
mν = minusv2u
2Y T
ν Mminus1R Yν
Inverting the seesaw equation gives Yν a la Casas amp Ibarra
Yν =radic
2i
vu
q
MR middotR middotp
mν middot Udagger
mν MR diagonal matrices containing the corresponding eigenvalues
U neutrino mixing matrix
R complex orthogonal matrix
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 13
ΦTP2Seesaw II
Below MGUT the superpotential reads
WII = WMSSM +1radic2(YT
bL bT1bL+ YS
bDcbS1
bDc) + YZbDc
bZ1bL
+1radic2(λ1
bHdbT1
bHd + λ2bHu
bT2bHu) +MT
bT1bT2 +MZ
bZ1bZ2 +MS
bS1bS2
fields with index 1 (2) originate from the 15-plet (15-plet)
The effective mass matrix is
mν = minusv2u
2
λ2
MTYT
Note that
YT = UT middot YT middot U
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 14
ΦTP2Seesaw III
In the SU(5) broken phase the superpotential becomes
WIII = WMSSM + bHu(cWMYN minusr
3
10bBMYB)bL+ bHu
bXMYXbDc
+1
2bBMMB
bBM +1
2bGMMG
bGM +1
2cWMMW
cWM + bXMMXbXM
giving
mν = minusv2u
2
bdquo
3
10Y T
B Mminus1B YB +
1
2Y T
WMminus1W YW
laquo
≃ minusv2u4
10Y T
WMminus1W YW
last step valid if MB ≃ MW and YB ≃ YW
rArr Casas-Ibarra decomposition for YW as in type-I up to factor 45
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 15
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
M1M
2M
3 (
Ge
V)
MSeesaw (GeV)
M1
M2
M3
0
500
1000
1500
2000
2500
1012
1013
1014
1015
1016
|MQ
||M
L||M
E| (G
eV
)MSeesaw (GeV)
|ME|
|ML|
|MQ|
750
1000
1250
1500
1750
2000
2250
1012
1013
1014
1015
1016
Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Overview
Flavour Generalities
LFV signals in models with
Dirac neutrinos
Majorana neutrinos
General MSSM + extensions
Squark flavour at LHC
Conclusions
More in F del Aguila et al EPJC 57 (2008) 183 [arXiv08011800]
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 2
ΦTP2Supersymmetry MSSM
Standard Model MSSM
mattere d d d
νe u u uhArr
e d d d
νe u u u
gauge sector hArrγ Z0 Wplusmn g γ z0 wplusmn g
Higgs sector hArrH0 h0hArrh0 H0 A0 Hplusmn h0d h0
u hplusmn
assume conserved R-Parity (minus1)(3(BminusL)+2s)
(γ z0 h0d h
0u) rarr χ0
i (wplusmn hplusmn) rarr χplusmnj
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 3
ΦTP2Flavour Generalities
SM Higgs doublet + Yukawa couplings
rArr after EWSB CKM- and PMNS matrices
rArr excellent agreement with data eg
BR(brarr sγ) BR(B+u rarr τ+ν) BR(Bs rarr micro+microminus) BR(B rarr Dτν)
BR(brarr smicro+microminus) BR(Bd rarr micro+microminus) BR(Bd rarr micro+microminus) ∆MBs ∆MBd
BR(Ds rarr τν) BR(Ds rarr microν) ∆MD
BR(K rarr microν) BR(K0L rarr π0νν) BR(K+ rarr π+νν) ∆mK ǫK
BR(τ rarr eγ) BR(τ rarr microγ) BR(τ rarr lllprime) (l lprime = e micro)
BR(microrarr eγ) BR(microminus rarr eminuse+eminus)
electric dipolemoments eg dn de
However no clue what determines sizes of masses and mixing angles
Supersymmetry eg MSSM
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus microHdHu
Vsoft = HdLTeelowast +HdQTdd
lowast +HuQTuulowast
+X
f=LeQdu
flowastM2ff +M2
Hd|Hu|2 +M2
Hu|Hu|2 minusBmicroHdHu
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 4
ΦTP2Flavour Generalities
Pragmatic approach Minimal Flavour Violationdagger
express all additional flavour structures in terms of rsquoknownrsquo Yukawas
eg at some (high) scale
Tf = A0fYf M2f
= M20f13 + αY dagger
f Yf
where A0f and M20f are scalars
generic prediction for squarkslowast FV decays are governed by |VCKMij |2 eg
BR(trarr χ+1 s) ≃ |VCKMts|2BR(trarr χ+
1 s)
BR(trarr χ012c) ltsim 10minus7
Sleptons depend on mechanism for neutrino masses
dagger AJ Buras et al PLB 500 (2001) 161 G DrsquoAmbrosio et al NPB 645 (2002) 155lowast E Lunghi WP O Vives PRD 74 (2006) 075003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 5
ΦTP2Flavour Generalities
more ambitious new symmetries eg Abelian or non-Abelian gauge or discrete
SU(3) flavour examplelowast
WY = Hψiψcj
h
θi3θ
j3 + θi
23θj23
ldquo
θ3θ3rdquo
+ ǫiklθ23kθ3lθj23
ldquo
θ23θ3rdquo
+ i
Yd prop
0
B
B
0 xd12 ε
3 xd13 ε
3
xd12 ε
3 ε2 xd23 ε
2
xd13 ε
3 xd23 ε
2 1
1
C
C
A
Yu prop
0
B
B
0 xu12 ε
3 xu13 ε
3
xu12 ε
3 ε2 xu23 ε
2
xu13 ε
3 xu23 ε
2 1
1
C
C
A
(M2f)ji = m2
0
bdquo
δji
+1
M2f
raquo
θdagger3iθj3 + θ3iθ
dagger3
j+ θdagger23i
θj23 + θ23iθ
dagger23
j+ θdagger123i
θj123 + θ123iθ
dagger123
jndash
+1
M4f
(ǫiklθdagger3
kθdagger23
l)(ǫjmnθ3mθ23n) +
laquo
LHC similar to MFV approach although somewhat larger effects
lowast GG Ross L Velasco-Sevilla O Vives NPB 692 50 (2004) L Calibbi J Jones-Perez
O Vives PRD 78 (2008) 075007 L Calibbi et al NPB 831 (2010) 26
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 6
ΦTP2Lepton flavour violation experimental data
Neutrinos tiny masses
∆m2atm ≃ 3 middot 10minus3 eV2
∆m2sol ≃ 7 middot 10minus5 eV2
3H decay mν ltsim 2 eV
Neutrinos large mixings
| tan θatm|2 ≃ 1
| tan θsol|2 ≃ 04
|Ue3|2 ltsim 005
strong bounds for charged leptons
BR(microrarr eγ) ltsim 12 middot 10minus11 BR(microminus rarr eminuse+eminus) ltsim 10minus12
BR(τ rarr eγ) ltsim 11 middot 10minus7 BR(τ rarr microγ) ltsim 68 middot 10minus8
BR(τ rarr lllprime) ltsim O(10minus8) (l lprime = e micro)
|de| ltsim 10minus27 e cm |dmicro| ltsim 15 middot 10minus18 e cm |dτ | ltsim 15 middot 10minus16 e cm
SUSY contributions to anomalous magnetic moments
|∆ae| le 10minus12 0 le ∆amicro le 43 middot 10minus10 |∆aτ | le 0058
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 7
ΦTP2Dirac neutrinos MFV scenario
analog to leptons or quarks
Yν H νL νR rarr Yν v νL νR = mν νL νR
requires Yν ≪ Ye
rArr no impact for future collider experiments
Exception νR is LSP and thus a candidate for dark matter
rArr long lived NLSP eg t1 rarr l+bνR
Remark mνRhardly runs rArr eg mνR
≃ m0 in mSUGRA
mνR ≃ 0 in GMSB
S Gopalakrishna A de Gouvea and W P JCAP 0605 (2006) 005 JHEP 0611 (2006) 050
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 8
ΦTP2Dirac neutrinos NLSP life times
m (GeV)12
βtan = 10
tan =30β
Lif
e t
ime (
seco
nd
s)
10
800 1000 1200 1400
100
600
1
τ1
m0 = 100 GeV
A0 = 100 GeV
sgn(micro) = 1
m (GeV)ν~1
t~
1
t~
1
m =300 GeV
t~
1
m =250 GeV
m =350 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
m (GeV)t~1
ν~
1
ν~
1
m =200 GeV
ν~
1
m =100 GeV
m =300 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
general signature two long lived particles + multi jets andor multi lepton
S K Gupta B Mukhopadhyaya S K Rai PRD 75 (2007) 075007
D Choudhury S K Gupta B Mukhopadhyaya PRD 78 (2008) 015023
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 9
ΦTP2Majorana neutrinos Seesaw mechanismlowast
Neutrino masses due tof
Λ(HL)(HL)
lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)
M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315
RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich
Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181
(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)
R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 10
ΦTP2The Setup GUT scale
Relevant SU(5) invariant parts of the superpotentials at MGUT
Type-I
WRHN = YIN Nc 5M middot 5H +
1
2MR NcNc
Type-II
W15H =1radic2Y
IIN 5M middot 15 middot 5M +
1radic2λ15H middot 15 middot 5H +
1radic2λ25H middot 15 middot 5H
+M1515 middot 15
Type-III
W24H = 5H24MY IIIN 5M +
1
224MM2424M
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 11
ΦTP2The SU(5)-broken phase
Under SU(3) times SUL(2) times U(1)Y
The 5 10 and 5H contain
5M = ( bDc bL) 10 = (bUc bEc bQ) 5H = ( bHc bHu) 5H = ( bHc bHd)
The 15 decomposes as
15 =bS(6 1minus2
3) + bT (1 3 1) + bZ(3 2
1
6)
The 24 decomposes as
24M =cWM (1 3 0) + bBM (1 1 0) + bXM (3 2minus5
6)
+ bXM (3 25
6) + bGM (8 1 0)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 12
ΦTP2Seesaw I
Postulate very heavy right-handed neutrinos yielding the following superpotential below
MGUT
WI =WMSSM +Wν
Wν = bNcYνbL middot bHu +
1
2bNcMR
bNc
Neutrino mass matrix
mν = minusv2u
2Y T
ν Mminus1R Yν
Inverting the seesaw equation gives Yν a la Casas amp Ibarra
Yν =radic
2i
vu
q
MR middotR middotp
mν middot Udagger
mν MR diagonal matrices containing the corresponding eigenvalues
U neutrino mixing matrix
R complex orthogonal matrix
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 13
ΦTP2Seesaw II
Below MGUT the superpotential reads
WII = WMSSM +1radic2(YT
bL bT1bL+ YS
bDcbS1
bDc) + YZbDc
bZ1bL
+1radic2(λ1
bHdbT1
bHd + λ2bHu
bT2bHu) +MT
bT1bT2 +MZ
bZ1bZ2 +MS
bS1bS2
fields with index 1 (2) originate from the 15-plet (15-plet)
The effective mass matrix is
mν = minusv2u
2
λ2
MTYT
Note that
YT = UT middot YT middot U
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 14
ΦTP2Seesaw III
In the SU(5) broken phase the superpotential becomes
WIII = WMSSM + bHu(cWMYN minusr
3
10bBMYB)bL+ bHu
bXMYXbDc
+1
2bBMMB
bBM +1
2bGMMG
bGM +1
2cWMMW
cWM + bXMMXbXM
giving
mν = minusv2u
2
bdquo
3
10Y T
B Mminus1B YB +
1
2Y T
WMminus1W YW
laquo
≃ minusv2u4
10Y T
WMminus1W YW
last step valid if MB ≃ MW and YB ≃ YW
rArr Casas-Ibarra decomposition for YW as in type-I up to factor 45
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 15
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
M1M
2M
3 (
Ge
V)
MSeesaw (GeV)
M1
M2
M3
0
500
1000
1500
2000
2500
1012
1013
1014
1015
1016
|MQ
||M
L||M
E| (G
eV
)MSeesaw (GeV)
|ME|
|ML|
|MQ|
750
1000
1250
1500
1750
2000
2250
1012
1013
1014
1015
1016
Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Supersymmetry MSSM
Standard Model MSSM
mattere d d d
νe u u uhArr
e d d d
νe u u u
gauge sector hArrγ Z0 Wplusmn g γ z0 wplusmn g
Higgs sector hArrH0 h0hArrh0 H0 A0 Hplusmn h0d h0
u hplusmn
assume conserved R-Parity (minus1)(3(BminusL)+2s)
(γ z0 h0d h
0u) rarr χ0
i (wplusmn hplusmn) rarr χplusmnj
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 3
ΦTP2Flavour Generalities
SM Higgs doublet + Yukawa couplings
rArr after EWSB CKM- and PMNS matrices
rArr excellent agreement with data eg
BR(brarr sγ) BR(B+u rarr τ+ν) BR(Bs rarr micro+microminus) BR(B rarr Dτν)
BR(brarr smicro+microminus) BR(Bd rarr micro+microminus) BR(Bd rarr micro+microminus) ∆MBs ∆MBd
BR(Ds rarr τν) BR(Ds rarr microν) ∆MD
BR(K rarr microν) BR(K0L rarr π0νν) BR(K+ rarr π+νν) ∆mK ǫK
BR(τ rarr eγ) BR(τ rarr microγ) BR(τ rarr lllprime) (l lprime = e micro)
BR(microrarr eγ) BR(microminus rarr eminuse+eminus)
electric dipolemoments eg dn de
However no clue what determines sizes of masses and mixing angles
Supersymmetry eg MSSM
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus microHdHu
Vsoft = HdLTeelowast +HdQTdd
lowast +HuQTuulowast
+X
f=LeQdu
flowastM2ff +M2
Hd|Hu|2 +M2
Hu|Hu|2 minusBmicroHdHu
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 4
ΦTP2Flavour Generalities
Pragmatic approach Minimal Flavour Violationdagger
express all additional flavour structures in terms of rsquoknownrsquo Yukawas
eg at some (high) scale
Tf = A0fYf M2f
= M20f13 + αY dagger
f Yf
where A0f and M20f are scalars
generic prediction for squarkslowast FV decays are governed by |VCKMij |2 eg
BR(trarr χ+1 s) ≃ |VCKMts|2BR(trarr χ+
1 s)
BR(trarr χ012c) ltsim 10minus7
Sleptons depend on mechanism for neutrino masses
dagger AJ Buras et al PLB 500 (2001) 161 G DrsquoAmbrosio et al NPB 645 (2002) 155lowast E Lunghi WP O Vives PRD 74 (2006) 075003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 5
ΦTP2Flavour Generalities
more ambitious new symmetries eg Abelian or non-Abelian gauge or discrete
SU(3) flavour examplelowast
WY = Hψiψcj
h
θi3θ
j3 + θi
23θj23
ldquo
θ3θ3rdquo
+ ǫiklθ23kθ3lθj23
ldquo
θ23θ3rdquo
+ i
Yd prop
0
B
B
0 xd12 ε
3 xd13 ε
3
xd12 ε
3 ε2 xd23 ε
2
xd13 ε
3 xd23 ε
2 1
1
C
C
A
Yu prop
0
B
B
0 xu12 ε
3 xu13 ε
3
xu12 ε
3 ε2 xu23 ε
2
xu13 ε
3 xu23 ε
2 1
1
C
C
A
(M2f)ji = m2
0
bdquo
δji
+1
M2f
raquo
θdagger3iθj3 + θ3iθ
dagger3
j+ θdagger23i
θj23 + θ23iθ
dagger23
j+ θdagger123i
θj123 + θ123iθ
dagger123
jndash
+1
M4f
(ǫiklθdagger3
kθdagger23
l)(ǫjmnθ3mθ23n) +
laquo
LHC similar to MFV approach although somewhat larger effects
lowast GG Ross L Velasco-Sevilla O Vives NPB 692 50 (2004) L Calibbi J Jones-Perez
O Vives PRD 78 (2008) 075007 L Calibbi et al NPB 831 (2010) 26
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 6
ΦTP2Lepton flavour violation experimental data
Neutrinos tiny masses
∆m2atm ≃ 3 middot 10minus3 eV2
∆m2sol ≃ 7 middot 10minus5 eV2
3H decay mν ltsim 2 eV
Neutrinos large mixings
| tan θatm|2 ≃ 1
| tan θsol|2 ≃ 04
|Ue3|2 ltsim 005
strong bounds for charged leptons
BR(microrarr eγ) ltsim 12 middot 10minus11 BR(microminus rarr eminuse+eminus) ltsim 10minus12
BR(τ rarr eγ) ltsim 11 middot 10minus7 BR(τ rarr microγ) ltsim 68 middot 10minus8
BR(τ rarr lllprime) ltsim O(10minus8) (l lprime = e micro)
|de| ltsim 10minus27 e cm |dmicro| ltsim 15 middot 10minus18 e cm |dτ | ltsim 15 middot 10minus16 e cm
SUSY contributions to anomalous magnetic moments
|∆ae| le 10minus12 0 le ∆amicro le 43 middot 10minus10 |∆aτ | le 0058
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 7
ΦTP2Dirac neutrinos MFV scenario
analog to leptons or quarks
Yν H νL νR rarr Yν v νL νR = mν νL νR
requires Yν ≪ Ye
rArr no impact for future collider experiments
Exception νR is LSP and thus a candidate for dark matter
rArr long lived NLSP eg t1 rarr l+bνR
Remark mνRhardly runs rArr eg mνR
≃ m0 in mSUGRA
mνR ≃ 0 in GMSB
S Gopalakrishna A de Gouvea and W P JCAP 0605 (2006) 005 JHEP 0611 (2006) 050
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 8
ΦTP2Dirac neutrinos NLSP life times
m (GeV)12
βtan = 10
tan =30β
Lif
e t
ime (
seco
nd
s)
10
800 1000 1200 1400
100
600
1
τ1
m0 = 100 GeV
A0 = 100 GeV
sgn(micro) = 1
m (GeV)ν~1
t~
1
t~
1
m =300 GeV
t~
1
m =250 GeV
m =350 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
m (GeV)t~1
ν~
1
ν~
1
m =200 GeV
ν~
1
m =100 GeV
m =300 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
general signature two long lived particles + multi jets andor multi lepton
S K Gupta B Mukhopadhyaya S K Rai PRD 75 (2007) 075007
D Choudhury S K Gupta B Mukhopadhyaya PRD 78 (2008) 015023
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 9
ΦTP2Majorana neutrinos Seesaw mechanismlowast
Neutrino masses due tof
Λ(HL)(HL)
lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)
M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315
RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich
Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181
(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)
R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 10
ΦTP2The Setup GUT scale
Relevant SU(5) invariant parts of the superpotentials at MGUT
Type-I
WRHN = YIN Nc 5M middot 5H +
1
2MR NcNc
Type-II
W15H =1radic2Y
IIN 5M middot 15 middot 5M +
1radic2λ15H middot 15 middot 5H +
1radic2λ25H middot 15 middot 5H
+M1515 middot 15
Type-III
W24H = 5H24MY IIIN 5M +
1
224MM2424M
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 11
ΦTP2The SU(5)-broken phase
Under SU(3) times SUL(2) times U(1)Y
The 5 10 and 5H contain
5M = ( bDc bL) 10 = (bUc bEc bQ) 5H = ( bHc bHu) 5H = ( bHc bHd)
The 15 decomposes as
15 =bS(6 1minus2
3) + bT (1 3 1) + bZ(3 2
1
6)
The 24 decomposes as
24M =cWM (1 3 0) + bBM (1 1 0) + bXM (3 2minus5
6)
+ bXM (3 25
6) + bGM (8 1 0)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 12
ΦTP2Seesaw I
Postulate very heavy right-handed neutrinos yielding the following superpotential below
MGUT
WI =WMSSM +Wν
Wν = bNcYνbL middot bHu +
1
2bNcMR
bNc
Neutrino mass matrix
mν = minusv2u
2Y T
ν Mminus1R Yν
Inverting the seesaw equation gives Yν a la Casas amp Ibarra
Yν =radic
2i
vu
q
MR middotR middotp
mν middot Udagger
mν MR diagonal matrices containing the corresponding eigenvalues
U neutrino mixing matrix
R complex orthogonal matrix
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 13
ΦTP2Seesaw II
Below MGUT the superpotential reads
WII = WMSSM +1radic2(YT
bL bT1bL+ YS
bDcbS1
bDc) + YZbDc
bZ1bL
+1radic2(λ1
bHdbT1
bHd + λ2bHu
bT2bHu) +MT
bT1bT2 +MZ
bZ1bZ2 +MS
bS1bS2
fields with index 1 (2) originate from the 15-plet (15-plet)
The effective mass matrix is
mν = minusv2u
2
λ2
MTYT
Note that
YT = UT middot YT middot U
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 14
ΦTP2Seesaw III
In the SU(5) broken phase the superpotential becomes
WIII = WMSSM + bHu(cWMYN minusr
3
10bBMYB)bL+ bHu
bXMYXbDc
+1
2bBMMB
bBM +1
2bGMMG
bGM +1
2cWMMW
cWM + bXMMXbXM
giving
mν = minusv2u
2
bdquo
3
10Y T
B Mminus1B YB +
1
2Y T
WMminus1W YW
laquo
≃ minusv2u4
10Y T
WMminus1W YW
last step valid if MB ≃ MW and YB ≃ YW
rArr Casas-Ibarra decomposition for YW as in type-I up to factor 45
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 15
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
M1M
2M
3 (
Ge
V)
MSeesaw (GeV)
M1
M2
M3
0
500
1000
1500
2000
2500
1012
1013
1014
1015
1016
|MQ
||M
L||M
E| (G
eV
)MSeesaw (GeV)
|ME|
|ML|
|MQ|
750
1000
1250
1500
1750
2000
2250
1012
1013
1014
1015
1016
Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Flavour Generalities
SM Higgs doublet + Yukawa couplings
rArr after EWSB CKM- and PMNS matrices
rArr excellent agreement with data eg
BR(brarr sγ) BR(B+u rarr τ+ν) BR(Bs rarr micro+microminus) BR(B rarr Dτν)
BR(brarr smicro+microminus) BR(Bd rarr micro+microminus) BR(Bd rarr micro+microminus) ∆MBs ∆MBd
BR(Ds rarr τν) BR(Ds rarr microν) ∆MD
BR(K rarr microν) BR(K0L rarr π0νν) BR(K+ rarr π+νν) ∆mK ǫK
BR(τ rarr eγ) BR(τ rarr microγ) BR(τ rarr lllprime) (l lprime = e micro)
BR(microrarr eγ) BR(microminus rarr eminuse+eminus)
electric dipolemoments eg dn de
However no clue what determines sizes of masses and mixing angles
Supersymmetry eg MSSM
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus microHdHu
Vsoft = HdLTeelowast +HdQTdd
lowast +HuQTuulowast
+X
f=LeQdu
flowastM2ff +M2
Hd|Hu|2 +M2
Hu|Hu|2 minusBmicroHdHu
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 4
ΦTP2Flavour Generalities
Pragmatic approach Minimal Flavour Violationdagger
express all additional flavour structures in terms of rsquoknownrsquo Yukawas
eg at some (high) scale
Tf = A0fYf M2f
= M20f13 + αY dagger
f Yf
where A0f and M20f are scalars
generic prediction for squarkslowast FV decays are governed by |VCKMij |2 eg
BR(trarr χ+1 s) ≃ |VCKMts|2BR(trarr χ+
1 s)
BR(trarr χ012c) ltsim 10minus7
Sleptons depend on mechanism for neutrino masses
dagger AJ Buras et al PLB 500 (2001) 161 G DrsquoAmbrosio et al NPB 645 (2002) 155lowast E Lunghi WP O Vives PRD 74 (2006) 075003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 5
ΦTP2Flavour Generalities
more ambitious new symmetries eg Abelian or non-Abelian gauge or discrete
SU(3) flavour examplelowast
WY = Hψiψcj
h
θi3θ
j3 + θi
23θj23
ldquo
θ3θ3rdquo
+ ǫiklθ23kθ3lθj23
ldquo
θ23θ3rdquo
+ i
Yd prop
0
B
B
0 xd12 ε
3 xd13 ε
3
xd12 ε
3 ε2 xd23 ε
2
xd13 ε
3 xd23 ε
2 1
1
C
C
A
Yu prop
0
B
B
0 xu12 ε
3 xu13 ε
3
xu12 ε
3 ε2 xu23 ε
2
xu13 ε
3 xu23 ε
2 1
1
C
C
A
(M2f)ji = m2
0
bdquo
δji
+1
M2f
raquo
θdagger3iθj3 + θ3iθ
dagger3
j+ θdagger23i
θj23 + θ23iθ
dagger23
j+ θdagger123i
θj123 + θ123iθ
dagger123
jndash
+1
M4f
(ǫiklθdagger3
kθdagger23
l)(ǫjmnθ3mθ23n) +
laquo
LHC similar to MFV approach although somewhat larger effects
lowast GG Ross L Velasco-Sevilla O Vives NPB 692 50 (2004) L Calibbi J Jones-Perez
O Vives PRD 78 (2008) 075007 L Calibbi et al NPB 831 (2010) 26
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 6
ΦTP2Lepton flavour violation experimental data
Neutrinos tiny masses
∆m2atm ≃ 3 middot 10minus3 eV2
∆m2sol ≃ 7 middot 10minus5 eV2
3H decay mν ltsim 2 eV
Neutrinos large mixings
| tan θatm|2 ≃ 1
| tan θsol|2 ≃ 04
|Ue3|2 ltsim 005
strong bounds for charged leptons
BR(microrarr eγ) ltsim 12 middot 10minus11 BR(microminus rarr eminuse+eminus) ltsim 10minus12
BR(τ rarr eγ) ltsim 11 middot 10minus7 BR(τ rarr microγ) ltsim 68 middot 10minus8
BR(τ rarr lllprime) ltsim O(10minus8) (l lprime = e micro)
|de| ltsim 10minus27 e cm |dmicro| ltsim 15 middot 10minus18 e cm |dτ | ltsim 15 middot 10minus16 e cm
SUSY contributions to anomalous magnetic moments
|∆ae| le 10minus12 0 le ∆amicro le 43 middot 10minus10 |∆aτ | le 0058
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 7
ΦTP2Dirac neutrinos MFV scenario
analog to leptons or quarks
Yν H νL νR rarr Yν v νL νR = mν νL νR
requires Yν ≪ Ye
rArr no impact for future collider experiments
Exception νR is LSP and thus a candidate for dark matter
rArr long lived NLSP eg t1 rarr l+bνR
Remark mνRhardly runs rArr eg mνR
≃ m0 in mSUGRA
mνR ≃ 0 in GMSB
S Gopalakrishna A de Gouvea and W P JCAP 0605 (2006) 005 JHEP 0611 (2006) 050
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 8
ΦTP2Dirac neutrinos NLSP life times
m (GeV)12
βtan = 10
tan =30β
Lif
e t
ime (
seco
nd
s)
10
800 1000 1200 1400
100
600
1
τ1
m0 = 100 GeV
A0 = 100 GeV
sgn(micro) = 1
m (GeV)ν~1
t~
1
t~
1
m =300 GeV
t~
1
m =250 GeV
m =350 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
m (GeV)t~1
ν~
1
ν~
1
m =200 GeV
ν~
1
m =100 GeV
m =300 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
general signature two long lived particles + multi jets andor multi lepton
S K Gupta B Mukhopadhyaya S K Rai PRD 75 (2007) 075007
D Choudhury S K Gupta B Mukhopadhyaya PRD 78 (2008) 015023
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 9
ΦTP2Majorana neutrinos Seesaw mechanismlowast
Neutrino masses due tof
Λ(HL)(HL)
lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)
M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315
RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich
Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181
(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)
R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 10
ΦTP2The Setup GUT scale
Relevant SU(5) invariant parts of the superpotentials at MGUT
Type-I
WRHN = YIN Nc 5M middot 5H +
1
2MR NcNc
Type-II
W15H =1radic2Y
IIN 5M middot 15 middot 5M +
1radic2λ15H middot 15 middot 5H +
1radic2λ25H middot 15 middot 5H
+M1515 middot 15
Type-III
W24H = 5H24MY IIIN 5M +
1
224MM2424M
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 11
ΦTP2The SU(5)-broken phase
Under SU(3) times SUL(2) times U(1)Y
The 5 10 and 5H contain
5M = ( bDc bL) 10 = (bUc bEc bQ) 5H = ( bHc bHu) 5H = ( bHc bHd)
The 15 decomposes as
15 =bS(6 1minus2
3) + bT (1 3 1) + bZ(3 2
1
6)
The 24 decomposes as
24M =cWM (1 3 0) + bBM (1 1 0) + bXM (3 2minus5
6)
+ bXM (3 25
6) + bGM (8 1 0)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 12
ΦTP2Seesaw I
Postulate very heavy right-handed neutrinos yielding the following superpotential below
MGUT
WI =WMSSM +Wν
Wν = bNcYνbL middot bHu +
1
2bNcMR
bNc
Neutrino mass matrix
mν = minusv2u
2Y T
ν Mminus1R Yν
Inverting the seesaw equation gives Yν a la Casas amp Ibarra
Yν =radic
2i
vu
q
MR middotR middotp
mν middot Udagger
mν MR diagonal matrices containing the corresponding eigenvalues
U neutrino mixing matrix
R complex orthogonal matrix
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 13
ΦTP2Seesaw II
Below MGUT the superpotential reads
WII = WMSSM +1radic2(YT
bL bT1bL+ YS
bDcbS1
bDc) + YZbDc
bZ1bL
+1radic2(λ1
bHdbT1
bHd + λ2bHu
bT2bHu) +MT
bT1bT2 +MZ
bZ1bZ2 +MS
bS1bS2
fields with index 1 (2) originate from the 15-plet (15-plet)
The effective mass matrix is
mν = minusv2u
2
λ2
MTYT
Note that
YT = UT middot YT middot U
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 14
ΦTP2Seesaw III
In the SU(5) broken phase the superpotential becomes
WIII = WMSSM + bHu(cWMYN minusr
3
10bBMYB)bL+ bHu
bXMYXbDc
+1
2bBMMB
bBM +1
2bGMMG
bGM +1
2cWMMW
cWM + bXMMXbXM
giving
mν = minusv2u
2
bdquo
3
10Y T
B Mminus1B YB +
1
2Y T
WMminus1W YW
laquo
≃ minusv2u4
10Y T
WMminus1W YW
last step valid if MB ≃ MW and YB ≃ YW
rArr Casas-Ibarra decomposition for YW as in type-I up to factor 45
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 15
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
M1M
2M
3 (
Ge
V)
MSeesaw (GeV)
M1
M2
M3
0
500
1000
1500
2000
2500
1012
1013
1014
1015
1016
|MQ
||M
L||M
E| (G
eV
)MSeesaw (GeV)
|ME|
|ML|
|MQ|
750
1000
1250
1500
1750
2000
2250
1012
1013
1014
1015
1016
Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Flavour Generalities
Pragmatic approach Minimal Flavour Violationdagger
express all additional flavour structures in terms of rsquoknownrsquo Yukawas
eg at some (high) scale
Tf = A0fYf M2f
= M20f13 + αY dagger
f Yf
where A0f and M20f are scalars
generic prediction for squarkslowast FV decays are governed by |VCKMij |2 eg
BR(trarr χ+1 s) ≃ |VCKMts|2BR(trarr χ+
1 s)
BR(trarr χ012c) ltsim 10minus7
Sleptons depend on mechanism for neutrino masses
dagger AJ Buras et al PLB 500 (2001) 161 G DrsquoAmbrosio et al NPB 645 (2002) 155lowast E Lunghi WP O Vives PRD 74 (2006) 075003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 5
ΦTP2Flavour Generalities
more ambitious new symmetries eg Abelian or non-Abelian gauge or discrete
SU(3) flavour examplelowast
WY = Hψiψcj
h
θi3θ
j3 + θi
23θj23
ldquo
θ3θ3rdquo
+ ǫiklθ23kθ3lθj23
ldquo
θ23θ3rdquo
+ i
Yd prop
0
B
B
0 xd12 ε
3 xd13 ε
3
xd12 ε
3 ε2 xd23 ε
2
xd13 ε
3 xd23 ε
2 1
1
C
C
A
Yu prop
0
B
B
0 xu12 ε
3 xu13 ε
3
xu12 ε
3 ε2 xu23 ε
2
xu13 ε
3 xu23 ε
2 1
1
C
C
A
(M2f)ji = m2
0
bdquo
δji
+1
M2f
raquo
θdagger3iθj3 + θ3iθ
dagger3
j+ θdagger23i
θj23 + θ23iθ
dagger23
j+ θdagger123i
θj123 + θ123iθ
dagger123
jndash
+1
M4f
(ǫiklθdagger3
kθdagger23
l)(ǫjmnθ3mθ23n) +
laquo
LHC similar to MFV approach although somewhat larger effects
lowast GG Ross L Velasco-Sevilla O Vives NPB 692 50 (2004) L Calibbi J Jones-Perez
O Vives PRD 78 (2008) 075007 L Calibbi et al NPB 831 (2010) 26
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 6
ΦTP2Lepton flavour violation experimental data
Neutrinos tiny masses
∆m2atm ≃ 3 middot 10minus3 eV2
∆m2sol ≃ 7 middot 10minus5 eV2
3H decay mν ltsim 2 eV
Neutrinos large mixings
| tan θatm|2 ≃ 1
| tan θsol|2 ≃ 04
|Ue3|2 ltsim 005
strong bounds for charged leptons
BR(microrarr eγ) ltsim 12 middot 10minus11 BR(microminus rarr eminuse+eminus) ltsim 10minus12
BR(τ rarr eγ) ltsim 11 middot 10minus7 BR(τ rarr microγ) ltsim 68 middot 10minus8
BR(τ rarr lllprime) ltsim O(10minus8) (l lprime = e micro)
|de| ltsim 10minus27 e cm |dmicro| ltsim 15 middot 10minus18 e cm |dτ | ltsim 15 middot 10minus16 e cm
SUSY contributions to anomalous magnetic moments
|∆ae| le 10minus12 0 le ∆amicro le 43 middot 10minus10 |∆aτ | le 0058
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 7
ΦTP2Dirac neutrinos MFV scenario
analog to leptons or quarks
Yν H νL νR rarr Yν v νL νR = mν νL νR
requires Yν ≪ Ye
rArr no impact for future collider experiments
Exception νR is LSP and thus a candidate for dark matter
rArr long lived NLSP eg t1 rarr l+bνR
Remark mνRhardly runs rArr eg mνR
≃ m0 in mSUGRA
mνR ≃ 0 in GMSB
S Gopalakrishna A de Gouvea and W P JCAP 0605 (2006) 005 JHEP 0611 (2006) 050
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 8
ΦTP2Dirac neutrinos NLSP life times
m (GeV)12
βtan = 10
tan =30β
Lif
e t
ime (
seco
nd
s)
10
800 1000 1200 1400
100
600
1
τ1
m0 = 100 GeV
A0 = 100 GeV
sgn(micro) = 1
m (GeV)ν~1
t~
1
t~
1
m =300 GeV
t~
1
m =250 GeV
m =350 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
m (GeV)t~1
ν~
1
ν~
1
m =200 GeV
ν~
1
m =100 GeV
m =300 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
general signature two long lived particles + multi jets andor multi lepton
S K Gupta B Mukhopadhyaya S K Rai PRD 75 (2007) 075007
D Choudhury S K Gupta B Mukhopadhyaya PRD 78 (2008) 015023
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 9
ΦTP2Majorana neutrinos Seesaw mechanismlowast
Neutrino masses due tof
Λ(HL)(HL)
lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)
M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315
RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich
Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181
(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)
R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 10
ΦTP2The Setup GUT scale
Relevant SU(5) invariant parts of the superpotentials at MGUT
Type-I
WRHN = YIN Nc 5M middot 5H +
1
2MR NcNc
Type-II
W15H =1radic2Y
IIN 5M middot 15 middot 5M +
1radic2λ15H middot 15 middot 5H +
1radic2λ25H middot 15 middot 5H
+M1515 middot 15
Type-III
W24H = 5H24MY IIIN 5M +
1
224MM2424M
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 11
ΦTP2The SU(5)-broken phase
Under SU(3) times SUL(2) times U(1)Y
The 5 10 and 5H contain
5M = ( bDc bL) 10 = (bUc bEc bQ) 5H = ( bHc bHu) 5H = ( bHc bHd)
The 15 decomposes as
15 =bS(6 1minus2
3) + bT (1 3 1) + bZ(3 2
1
6)
The 24 decomposes as
24M =cWM (1 3 0) + bBM (1 1 0) + bXM (3 2minus5
6)
+ bXM (3 25
6) + bGM (8 1 0)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 12
ΦTP2Seesaw I
Postulate very heavy right-handed neutrinos yielding the following superpotential below
MGUT
WI =WMSSM +Wν
Wν = bNcYνbL middot bHu +
1
2bNcMR
bNc
Neutrino mass matrix
mν = minusv2u
2Y T
ν Mminus1R Yν
Inverting the seesaw equation gives Yν a la Casas amp Ibarra
Yν =radic
2i
vu
q
MR middotR middotp
mν middot Udagger
mν MR diagonal matrices containing the corresponding eigenvalues
U neutrino mixing matrix
R complex orthogonal matrix
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 13
ΦTP2Seesaw II
Below MGUT the superpotential reads
WII = WMSSM +1radic2(YT
bL bT1bL+ YS
bDcbS1
bDc) + YZbDc
bZ1bL
+1radic2(λ1
bHdbT1
bHd + λ2bHu
bT2bHu) +MT
bT1bT2 +MZ
bZ1bZ2 +MS
bS1bS2
fields with index 1 (2) originate from the 15-plet (15-plet)
The effective mass matrix is
mν = minusv2u
2
λ2
MTYT
Note that
YT = UT middot YT middot U
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 14
ΦTP2Seesaw III
In the SU(5) broken phase the superpotential becomes
WIII = WMSSM + bHu(cWMYN minusr
3
10bBMYB)bL+ bHu
bXMYXbDc
+1
2bBMMB
bBM +1
2bGMMG
bGM +1
2cWMMW
cWM + bXMMXbXM
giving
mν = minusv2u
2
bdquo
3
10Y T
B Mminus1B YB +
1
2Y T
WMminus1W YW
laquo
≃ minusv2u4
10Y T
WMminus1W YW
last step valid if MB ≃ MW and YB ≃ YW
rArr Casas-Ibarra decomposition for YW as in type-I up to factor 45
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 15
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
M1M
2M
3 (
Ge
V)
MSeesaw (GeV)
M1
M2
M3
0
500
1000
1500
2000
2500
1012
1013
1014
1015
1016
|MQ
||M
L||M
E| (G
eV
)MSeesaw (GeV)
|ME|
|ML|
|MQ|
750
1000
1250
1500
1750
2000
2250
1012
1013
1014
1015
1016
Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Flavour Generalities
more ambitious new symmetries eg Abelian or non-Abelian gauge or discrete
SU(3) flavour examplelowast
WY = Hψiψcj
h
θi3θ
j3 + θi
23θj23
ldquo
θ3θ3rdquo
+ ǫiklθ23kθ3lθj23
ldquo
θ23θ3rdquo
+ i
Yd prop
0
B
B
0 xd12 ε
3 xd13 ε
3
xd12 ε
3 ε2 xd23 ε
2
xd13 ε
3 xd23 ε
2 1
1
C
C
A
Yu prop
0
B
B
0 xu12 ε
3 xu13 ε
3
xu12 ε
3 ε2 xu23 ε
2
xu13 ε
3 xu23 ε
2 1
1
C
C
A
(M2f)ji = m2
0
bdquo
δji
+1
M2f
raquo
θdagger3iθj3 + θ3iθ
dagger3
j+ θdagger23i
θj23 + θ23iθ
dagger23
j+ θdagger123i
θj123 + θ123iθ
dagger123
jndash
+1
M4f
(ǫiklθdagger3
kθdagger23
l)(ǫjmnθ3mθ23n) +
laquo
LHC similar to MFV approach although somewhat larger effects
lowast GG Ross L Velasco-Sevilla O Vives NPB 692 50 (2004) L Calibbi J Jones-Perez
O Vives PRD 78 (2008) 075007 L Calibbi et al NPB 831 (2010) 26
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 6
ΦTP2Lepton flavour violation experimental data
Neutrinos tiny masses
∆m2atm ≃ 3 middot 10minus3 eV2
∆m2sol ≃ 7 middot 10minus5 eV2
3H decay mν ltsim 2 eV
Neutrinos large mixings
| tan θatm|2 ≃ 1
| tan θsol|2 ≃ 04
|Ue3|2 ltsim 005
strong bounds for charged leptons
BR(microrarr eγ) ltsim 12 middot 10minus11 BR(microminus rarr eminuse+eminus) ltsim 10minus12
BR(τ rarr eγ) ltsim 11 middot 10minus7 BR(τ rarr microγ) ltsim 68 middot 10minus8
BR(τ rarr lllprime) ltsim O(10minus8) (l lprime = e micro)
|de| ltsim 10minus27 e cm |dmicro| ltsim 15 middot 10minus18 e cm |dτ | ltsim 15 middot 10minus16 e cm
SUSY contributions to anomalous magnetic moments
|∆ae| le 10minus12 0 le ∆amicro le 43 middot 10minus10 |∆aτ | le 0058
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 7
ΦTP2Dirac neutrinos MFV scenario
analog to leptons or quarks
Yν H νL νR rarr Yν v νL νR = mν νL νR
requires Yν ≪ Ye
rArr no impact for future collider experiments
Exception νR is LSP and thus a candidate for dark matter
rArr long lived NLSP eg t1 rarr l+bνR
Remark mνRhardly runs rArr eg mνR
≃ m0 in mSUGRA
mνR ≃ 0 in GMSB
S Gopalakrishna A de Gouvea and W P JCAP 0605 (2006) 005 JHEP 0611 (2006) 050
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 8
ΦTP2Dirac neutrinos NLSP life times
m (GeV)12
βtan = 10
tan =30β
Lif
e t
ime (
seco
nd
s)
10
800 1000 1200 1400
100
600
1
τ1
m0 = 100 GeV
A0 = 100 GeV
sgn(micro) = 1
m (GeV)ν~1
t~
1
t~
1
m =300 GeV
t~
1
m =250 GeV
m =350 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
m (GeV)t~1
ν~
1
ν~
1
m =200 GeV
ν~
1
m =100 GeV
m =300 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
general signature two long lived particles + multi jets andor multi lepton
S K Gupta B Mukhopadhyaya S K Rai PRD 75 (2007) 075007
D Choudhury S K Gupta B Mukhopadhyaya PRD 78 (2008) 015023
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 9
ΦTP2Majorana neutrinos Seesaw mechanismlowast
Neutrino masses due tof
Λ(HL)(HL)
lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)
M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315
RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich
Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181
(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)
R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 10
ΦTP2The Setup GUT scale
Relevant SU(5) invariant parts of the superpotentials at MGUT
Type-I
WRHN = YIN Nc 5M middot 5H +
1
2MR NcNc
Type-II
W15H =1radic2Y
IIN 5M middot 15 middot 5M +
1radic2λ15H middot 15 middot 5H +
1radic2λ25H middot 15 middot 5H
+M1515 middot 15
Type-III
W24H = 5H24MY IIIN 5M +
1
224MM2424M
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 11
ΦTP2The SU(5)-broken phase
Under SU(3) times SUL(2) times U(1)Y
The 5 10 and 5H contain
5M = ( bDc bL) 10 = (bUc bEc bQ) 5H = ( bHc bHu) 5H = ( bHc bHd)
The 15 decomposes as
15 =bS(6 1minus2
3) + bT (1 3 1) + bZ(3 2
1
6)
The 24 decomposes as
24M =cWM (1 3 0) + bBM (1 1 0) + bXM (3 2minus5
6)
+ bXM (3 25
6) + bGM (8 1 0)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 12
ΦTP2Seesaw I
Postulate very heavy right-handed neutrinos yielding the following superpotential below
MGUT
WI =WMSSM +Wν
Wν = bNcYνbL middot bHu +
1
2bNcMR
bNc
Neutrino mass matrix
mν = minusv2u
2Y T
ν Mminus1R Yν
Inverting the seesaw equation gives Yν a la Casas amp Ibarra
Yν =radic
2i
vu
q
MR middotR middotp
mν middot Udagger
mν MR diagonal matrices containing the corresponding eigenvalues
U neutrino mixing matrix
R complex orthogonal matrix
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 13
ΦTP2Seesaw II
Below MGUT the superpotential reads
WII = WMSSM +1radic2(YT
bL bT1bL+ YS
bDcbS1
bDc) + YZbDc
bZ1bL
+1radic2(λ1
bHdbT1
bHd + λ2bHu
bT2bHu) +MT
bT1bT2 +MZ
bZ1bZ2 +MS
bS1bS2
fields with index 1 (2) originate from the 15-plet (15-plet)
The effective mass matrix is
mν = minusv2u
2
λ2
MTYT
Note that
YT = UT middot YT middot U
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 14
ΦTP2Seesaw III
In the SU(5) broken phase the superpotential becomes
WIII = WMSSM + bHu(cWMYN minusr
3
10bBMYB)bL+ bHu
bXMYXbDc
+1
2bBMMB
bBM +1
2bGMMG
bGM +1
2cWMMW
cWM + bXMMXbXM
giving
mν = minusv2u
2
bdquo
3
10Y T
B Mminus1B YB +
1
2Y T
WMminus1W YW
laquo
≃ minusv2u4
10Y T
WMminus1W YW
last step valid if MB ≃ MW and YB ≃ YW
rArr Casas-Ibarra decomposition for YW as in type-I up to factor 45
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 15
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
M1M
2M
3 (
Ge
V)
MSeesaw (GeV)
M1
M2
M3
0
500
1000
1500
2000
2500
1012
1013
1014
1015
1016
|MQ
||M
L||M
E| (G
eV
)MSeesaw (GeV)
|ME|
|ML|
|MQ|
750
1000
1250
1500
1750
2000
2250
1012
1013
1014
1015
1016
Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Lepton flavour violation experimental data
Neutrinos tiny masses
∆m2atm ≃ 3 middot 10minus3 eV2
∆m2sol ≃ 7 middot 10minus5 eV2
3H decay mν ltsim 2 eV
Neutrinos large mixings
| tan θatm|2 ≃ 1
| tan θsol|2 ≃ 04
|Ue3|2 ltsim 005
strong bounds for charged leptons
BR(microrarr eγ) ltsim 12 middot 10minus11 BR(microminus rarr eminuse+eminus) ltsim 10minus12
BR(τ rarr eγ) ltsim 11 middot 10minus7 BR(τ rarr microγ) ltsim 68 middot 10minus8
BR(τ rarr lllprime) ltsim O(10minus8) (l lprime = e micro)
|de| ltsim 10minus27 e cm |dmicro| ltsim 15 middot 10minus18 e cm |dτ | ltsim 15 middot 10minus16 e cm
SUSY contributions to anomalous magnetic moments
|∆ae| le 10minus12 0 le ∆amicro le 43 middot 10minus10 |∆aτ | le 0058
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 7
ΦTP2Dirac neutrinos MFV scenario
analog to leptons or quarks
Yν H νL νR rarr Yν v νL νR = mν νL νR
requires Yν ≪ Ye
rArr no impact for future collider experiments
Exception νR is LSP and thus a candidate for dark matter
rArr long lived NLSP eg t1 rarr l+bνR
Remark mνRhardly runs rArr eg mνR
≃ m0 in mSUGRA
mνR ≃ 0 in GMSB
S Gopalakrishna A de Gouvea and W P JCAP 0605 (2006) 005 JHEP 0611 (2006) 050
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 8
ΦTP2Dirac neutrinos NLSP life times
m (GeV)12
βtan = 10
tan =30β
Lif
e t
ime (
seco
nd
s)
10
800 1000 1200 1400
100
600
1
τ1
m0 = 100 GeV
A0 = 100 GeV
sgn(micro) = 1
m (GeV)ν~1
t~
1
t~
1
m =300 GeV
t~
1
m =250 GeV
m =350 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
m (GeV)t~1
ν~
1
ν~
1
m =200 GeV
ν~
1
m =100 GeV
m =300 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
general signature two long lived particles + multi jets andor multi lepton
S K Gupta B Mukhopadhyaya S K Rai PRD 75 (2007) 075007
D Choudhury S K Gupta B Mukhopadhyaya PRD 78 (2008) 015023
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 9
ΦTP2Majorana neutrinos Seesaw mechanismlowast
Neutrino masses due tof
Λ(HL)(HL)
lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)
M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315
RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich
Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181
(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)
R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 10
ΦTP2The Setup GUT scale
Relevant SU(5) invariant parts of the superpotentials at MGUT
Type-I
WRHN = YIN Nc 5M middot 5H +
1
2MR NcNc
Type-II
W15H =1radic2Y
IIN 5M middot 15 middot 5M +
1radic2λ15H middot 15 middot 5H +
1radic2λ25H middot 15 middot 5H
+M1515 middot 15
Type-III
W24H = 5H24MY IIIN 5M +
1
224MM2424M
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 11
ΦTP2The SU(5)-broken phase
Under SU(3) times SUL(2) times U(1)Y
The 5 10 and 5H contain
5M = ( bDc bL) 10 = (bUc bEc bQ) 5H = ( bHc bHu) 5H = ( bHc bHd)
The 15 decomposes as
15 =bS(6 1minus2
3) + bT (1 3 1) + bZ(3 2
1
6)
The 24 decomposes as
24M =cWM (1 3 0) + bBM (1 1 0) + bXM (3 2minus5
6)
+ bXM (3 25
6) + bGM (8 1 0)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 12
ΦTP2Seesaw I
Postulate very heavy right-handed neutrinos yielding the following superpotential below
MGUT
WI =WMSSM +Wν
Wν = bNcYνbL middot bHu +
1
2bNcMR
bNc
Neutrino mass matrix
mν = minusv2u
2Y T
ν Mminus1R Yν
Inverting the seesaw equation gives Yν a la Casas amp Ibarra
Yν =radic
2i
vu
q
MR middotR middotp
mν middot Udagger
mν MR diagonal matrices containing the corresponding eigenvalues
U neutrino mixing matrix
R complex orthogonal matrix
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 13
ΦTP2Seesaw II
Below MGUT the superpotential reads
WII = WMSSM +1radic2(YT
bL bT1bL+ YS
bDcbS1
bDc) + YZbDc
bZ1bL
+1radic2(λ1
bHdbT1
bHd + λ2bHu
bT2bHu) +MT
bT1bT2 +MZ
bZ1bZ2 +MS
bS1bS2
fields with index 1 (2) originate from the 15-plet (15-plet)
The effective mass matrix is
mν = minusv2u
2
λ2
MTYT
Note that
YT = UT middot YT middot U
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 14
ΦTP2Seesaw III
In the SU(5) broken phase the superpotential becomes
WIII = WMSSM + bHu(cWMYN minusr
3
10bBMYB)bL+ bHu
bXMYXbDc
+1
2bBMMB
bBM +1
2bGMMG
bGM +1
2cWMMW
cWM + bXMMXbXM
giving
mν = minusv2u
2
bdquo
3
10Y T
B Mminus1B YB +
1
2Y T
WMminus1W YW
laquo
≃ minusv2u4
10Y T
WMminus1W YW
last step valid if MB ≃ MW and YB ≃ YW
rArr Casas-Ibarra decomposition for YW as in type-I up to factor 45
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 15
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
M1M
2M
3 (
Ge
V)
MSeesaw (GeV)
M1
M2
M3
0
500
1000
1500
2000
2500
1012
1013
1014
1015
1016
|MQ
||M
L||M
E| (G
eV
)MSeesaw (GeV)
|ME|
|ML|
|MQ|
750
1000
1250
1500
1750
2000
2250
1012
1013
1014
1015
1016
Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Dirac neutrinos MFV scenario
analog to leptons or quarks
Yν H νL νR rarr Yν v νL νR = mν νL νR
requires Yν ≪ Ye
rArr no impact for future collider experiments
Exception νR is LSP and thus a candidate for dark matter
rArr long lived NLSP eg t1 rarr l+bνR
Remark mνRhardly runs rArr eg mνR
≃ m0 in mSUGRA
mνR ≃ 0 in GMSB
S Gopalakrishna A de Gouvea and W P JCAP 0605 (2006) 005 JHEP 0611 (2006) 050
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 8
ΦTP2Dirac neutrinos NLSP life times
m (GeV)12
βtan = 10
tan =30β
Lif
e t
ime (
seco
nd
s)
10
800 1000 1200 1400
100
600
1
τ1
m0 = 100 GeV
A0 = 100 GeV
sgn(micro) = 1
m (GeV)ν~1
t~
1
t~
1
m =300 GeV
t~
1
m =250 GeV
m =350 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
m (GeV)t~1
ν~
1
ν~
1
m =200 GeV
ν~
1
m =100 GeV
m =300 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
general signature two long lived particles + multi jets andor multi lepton
S K Gupta B Mukhopadhyaya S K Rai PRD 75 (2007) 075007
D Choudhury S K Gupta B Mukhopadhyaya PRD 78 (2008) 015023
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 9
ΦTP2Majorana neutrinos Seesaw mechanismlowast
Neutrino masses due tof
Λ(HL)(HL)
lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)
M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315
RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich
Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181
(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)
R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 10
ΦTP2The Setup GUT scale
Relevant SU(5) invariant parts of the superpotentials at MGUT
Type-I
WRHN = YIN Nc 5M middot 5H +
1
2MR NcNc
Type-II
W15H =1radic2Y
IIN 5M middot 15 middot 5M +
1radic2λ15H middot 15 middot 5H +
1radic2λ25H middot 15 middot 5H
+M1515 middot 15
Type-III
W24H = 5H24MY IIIN 5M +
1
224MM2424M
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 11
ΦTP2The SU(5)-broken phase
Under SU(3) times SUL(2) times U(1)Y
The 5 10 and 5H contain
5M = ( bDc bL) 10 = (bUc bEc bQ) 5H = ( bHc bHu) 5H = ( bHc bHd)
The 15 decomposes as
15 =bS(6 1minus2
3) + bT (1 3 1) + bZ(3 2
1
6)
The 24 decomposes as
24M =cWM (1 3 0) + bBM (1 1 0) + bXM (3 2minus5
6)
+ bXM (3 25
6) + bGM (8 1 0)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 12
ΦTP2Seesaw I
Postulate very heavy right-handed neutrinos yielding the following superpotential below
MGUT
WI =WMSSM +Wν
Wν = bNcYνbL middot bHu +
1
2bNcMR
bNc
Neutrino mass matrix
mν = minusv2u
2Y T
ν Mminus1R Yν
Inverting the seesaw equation gives Yν a la Casas amp Ibarra
Yν =radic
2i
vu
q
MR middotR middotp
mν middot Udagger
mν MR diagonal matrices containing the corresponding eigenvalues
U neutrino mixing matrix
R complex orthogonal matrix
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 13
ΦTP2Seesaw II
Below MGUT the superpotential reads
WII = WMSSM +1radic2(YT
bL bT1bL+ YS
bDcbS1
bDc) + YZbDc
bZ1bL
+1radic2(λ1
bHdbT1
bHd + λ2bHu
bT2bHu) +MT
bT1bT2 +MZ
bZ1bZ2 +MS
bS1bS2
fields with index 1 (2) originate from the 15-plet (15-plet)
The effective mass matrix is
mν = minusv2u
2
λ2
MTYT
Note that
YT = UT middot YT middot U
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 14
ΦTP2Seesaw III
In the SU(5) broken phase the superpotential becomes
WIII = WMSSM + bHu(cWMYN minusr
3
10bBMYB)bL+ bHu
bXMYXbDc
+1
2bBMMB
bBM +1
2bGMMG
bGM +1
2cWMMW
cWM + bXMMXbXM
giving
mν = minusv2u
2
bdquo
3
10Y T
B Mminus1B YB +
1
2Y T
WMminus1W YW
laquo
≃ minusv2u4
10Y T
WMminus1W YW
last step valid if MB ≃ MW and YB ≃ YW
rArr Casas-Ibarra decomposition for YW as in type-I up to factor 45
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 15
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
M1M
2M
3 (
Ge
V)
MSeesaw (GeV)
M1
M2
M3
0
500
1000
1500
2000
2500
1012
1013
1014
1015
1016
|MQ
||M
L||M
E| (G
eV
)MSeesaw (GeV)
|ME|
|ML|
|MQ|
750
1000
1250
1500
1750
2000
2250
1012
1013
1014
1015
1016
Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Dirac neutrinos NLSP life times
m (GeV)12
βtan = 10
tan =30β
Lif
e t
ime (
seco
nd
s)
10
800 1000 1200 1400
100
600
1
τ1
m0 = 100 GeV
A0 = 100 GeV
sgn(micro) = 1
m (GeV)ν~1
t~
1
t~
1
m =300 GeV
t~
1
m =250 GeV
m =350 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
m (GeV)t~1
ν~
1
ν~
1
m =200 GeV
ν~
1
m =100 GeV
m =300 GeV
100
10000
1e+06
1e+08
1e+10
1e+12
1e+14
100 150 200 250 300 350
Lif
eminus
tim
e (
secon
ds)
general signature two long lived particles + multi jets andor multi lepton
S K Gupta B Mukhopadhyaya S K Rai PRD 75 (2007) 075007
D Choudhury S K Gupta B Mukhopadhyaya PRD 78 (2008) 015023
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 9
ΦTP2Majorana neutrinos Seesaw mechanismlowast
Neutrino masses due tof
Λ(HL)(HL)
lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)
M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315
RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich
Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181
(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)
R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 10
ΦTP2The Setup GUT scale
Relevant SU(5) invariant parts of the superpotentials at MGUT
Type-I
WRHN = YIN Nc 5M middot 5H +
1
2MR NcNc
Type-II
W15H =1radic2Y
IIN 5M middot 15 middot 5M +
1radic2λ15H middot 15 middot 5H +
1radic2λ25H middot 15 middot 5H
+M1515 middot 15
Type-III
W24H = 5H24MY IIIN 5M +
1
224MM2424M
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 11
ΦTP2The SU(5)-broken phase
Under SU(3) times SUL(2) times U(1)Y
The 5 10 and 5H contain
5M = ( bDc bL) 10 = (bUc bEc bQ) 5H = ( bHc bHu) 5H = ( bHc bHd)
The 15 decomposes as
15 =bS(6 1minus2
3) + bT (1 3 1) + bZ(3 2
1
6)
The 24 decomposes as
24M =cWM (1 3 0) + bBM (1 1 0) + bXM (3 2minus5
6)
+ bXM (3 25
6) + bGM (8 1 0)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 12
ΦTP2Seesaw I
Postulate very heavy right-handed neutrinos yielding the following superpotential below
MGUT
WI =WMSSM +Wν
Wν = bNcYνbL middot bHu +
1
2bNcMR
bNc
Neutrino mass matrix
mν = minusv2u
2Y T
ν Mminus1R Yν
Inverting the seesaw equation gives Yν a la Casas amp Ibarra
Yν =radic
2i
vu
q
MR middotR middotp
mν middot Udagger
mν MR diagonal matrices containing the corresponding eigenvalues
U neutrino mixing matrix
R complex orthogonal matrix
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 13
ΦTP2Seesaw II
Below MGUT the superpotential reads
WII = WMSSM +1radic2(YT
bL bT1bL+ YS
bDcbS1
bDc) + YZbDc
bZ1bL
+1radic2(λ1
bHdbT1
bHd + λ2bHu
bT2bHu) +MT
bT1bT2 +MZ
bZ1bZ2 +MS
bS1bS2
fields with index 1 (2) originate from the 15-plet (15-plet)
The effective mass matrix is
mν = minusv2u
2
λ2
MTYT
Note that
YT = UT middot YT middot U
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 14
ΦTP2Seesaw III
In the SU(5) broken phase the superpotential becomes
WIII = WMSSM + bHu(cWMYN minusr
3
10bBMYB)bL+ bHu
bXMYXbDc
+1
2bBMMB
bBM +1
2bGMMG
bGM +1
2cWMMW
cWM + bXMMXbXM
giving
mν = minusv2u
2
bdquo
3
10Y T
B Mminus1B YB +
1
2Y T
WMminus1W YW
laquo
≃ minusv2u4
10Y T
WMminus1W YW
last step valid if MB ≃ MW and YB ≃ YW
rArr Casas-Ibarra decomposition for YW as in type-I up to factor 45
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 15
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
M1M
2M
3 (
Ge
V)
MSeesaw (GeV)
M1
M2
M3
0
500
1000
1500
2000
2500
1012
1013
1014
1015
1016
|MQ
||M
L||M
E| (G
eV
)MSeesaw (GeV)
|ME|
|ML|
|MQ|
750
1000
1250
1500
1750
2000
2250
1012
1013
1014
1015
1016
Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Majorana neutrinos Seesaw mechanismlowast
Neutrino masses due tof
Λ(HL)(HL)
lowast P Minkowski Phys Lett B 67 (1977) 421 T Yanagida KEK-report 79-18 (1979)
M Gell-Mann P Ramond R Slansky in Supergravity North Holland (1979) p 315
RN Mohapatra and G Senjanovic Phys Rev Lett 44 912 (1980) M Magg and CWetterich
Phys Lett B 94 (1980) 61 G Lazarides Q Shafi and C Wetterich Nucl Phys B 181
(1981) 287 J Schechter and J W F Valle Phys Rev D25 774 (1982)
R Foot H Lew X G He and G C Joshi Z Phys C 44 (1989) 441
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 10
ΦTP2The Setup GUT scale
Relevant SU(5) invariant parts of the superpotentials at MGUT
Type-I
WRHN = YIN Nc 5M middot 5H +
1
2MR NcNc
Type-II
W15H =1radic2Y
IIN 5M middot 15 middot 5M +
1radic2λ15H middot 15 middot 5H +
1radic2λ25H middot 15 middot 5H
+M1515 middot 15
Type-III
W24H = 5H24MY IIIN 5M +
1
224MM2424M
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 11
ΦTP2The SU(5)-broken phase
Under SU(3) times SUL(2) times U(1)Y
The 5 10 and 5H contain
5M = ( bDc bL) 10 = (bUc bEc bQ) 5H = ( bHc bHu) 5H = ( bHc bHd)
The 15 decomposes as
15 =bS(6 1minus2
3) + bT (1 3 1) + bZ(3 2
1
6)
The 24 decomposes as
24M =cWM (1 3 0) + bBM (1 1 0) + bXM (3 2minus5
6)
+ bXM (3 25
6) + bGM (8 1 0)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 12
ΦTP2Seesaw I
Postulate very heavy right-handed neutrinos yielding the following superpotential below
MGUT
WI =WMSSM +Wν
Wν = bNcYνbL middot bHu +
1
2bNcMR
bNc
Neutrino mass matrix
mν = minusv2u
2Y T
ν Mminus1R Yν
Inverting the seesaw equation gives Yν a la Casas amp Ibarra
Yν =radic
2i
vu
q
MR middotR middotp
mν middot Udagger
mν MR diagonal matrices containing the corresponding eigenvalues
U neutrino mixing matrix
R complex orthogonal matrix
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 13
ΦTP2Seesaw II
Below MGUT the superpotential reads
WII = WMSSM +1radic2(YT
bL bT1bL+ YS
bDcbS1
bDc) + YZbDc
bZ1bL
+1radic2(λ1
bHdbT1
bHd + λ2bHu
bT2bHu) +MT
bT1bT2 +MZ
bZ1bZ2 +MS
bS1bS2
fields with index 1 (2) originate from the 15-plet (15-plet)
The effective mass matrix is
mν = minusv2u
2
λ2
MTYT
Note that
YT = UT middot YT middot U
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 14
ΦTP2Seesaw III
In the SU(5) broken phase the superpotential becomes
WIII = WMSSM + bHu(cWMYN minusr
3
10bBMYB)bL+ bHu
bXMYXbDc
+1
2bBMMB
bBM +1
2bGMMG
bGM +1
2cWMMW
cWM + bXMMXbXM
giving
mν = minusv2u
2
bdquo
3
10Y T
B Mminus1B YB +
1
2Y T
WMminus1W YW
laquo
≃ minusv2u4
10Y T
WMminus1W YW
last step valid if MB ≃ MW and YB ≃ YW
rArr Casas-Ibarra decomposition for YW as in type-I up to factor 45
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 15
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
M1M
2M
3 (
Ge
V)
MSeesaw (GeV)
M1
M2
M3
0
500
1000
1500
2000
2500
1012
1013
1014
1015
1016
|MQ
||M
L||M
E| (G
eV
)MSeesaw (GeV)
|ME|
|ML|
|MQ|
750
1000
1250
1500
1750
2000
2250
1012
1013
1014
1015
1016
Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2The Setup GUT scale
Relevant SU(5) invariant parts of the superpotentials at MGUT
Type-I
WRHN = YIN Nc 5M middot 5H +
1
2MR NcNc
Type-II
W15H =1radic2Y
IIN 5M middot 15 middot 5M +
1radic2λ15H middot 15 middot 5H +
1radic2λ25H middot 15 middot 5H
+M1515 middot 15
Type-III
W24H = 5H24MY IIIN 5M +
1
224MM2424M
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 11
ΦTP2The SU(5)-broken phase
Under SU(3) times SUL(2) times U(1)Y
The 5 10 and 5H contain
5M = ( bDc bL) 10 = (bUc bEc bQ) 5H = ( bHc bHu) 5H = ( bHc bHd)
The 15 decomposes as
15 =bS(6 1minus2
3) + bT (1 3 1) + bZ(3 2
1
6)
The 24 decomposes as
24M =cWM (1 3 0) + bBM (1 1 0) + bXM (3 2minus5
6)
+ bXM (3 25
6) + bGM (8 1 0)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 12
ΦTP2Seesaw I
Postulate very heavy right-handed neutrinos yielding the following superpotential below
MGUT
WI =WMSSM +Wν
Wν = bNcYνbL middot bHu +
1
2bNcMR
bNc
Neutrino mass matrix
mν = minusv2u
2Y T
ν Mminus1R Yν
Inverting the seesaw equation gives Yν a la Casas amp Ibarra
Yν =radic
2i
vu
q
MR middotR middotp
mν middot Udagger
mν MR diagonal matrices containing the corresponding eigenvalues
U neutrino mixing matrix
R complex orthogonal matrix
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 13
ΦTP2Seesaw II
Below MGUT the superpotential reads
WII = WMSSM +1radic2(YT
bL bT1bL+ YS
bDcbS1
bDc) + YZbDc
bZ1bL
+1radic2(λ1
bHdbT1
bHd + λ2bHu
bT2bHu) +MT
bT1bT2 +MZ
bZ1bZ2 +MS
bS1bS2
fields with index 1 (2) originate from the 15-plet (15-plet)
The effective mass matrix is
mν = minusv2u
2
λ2
MTYT
Note that
YT = UT middot YT middot U
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 14
ΦTP2Seesaw III
In the SU(5) broken phase the superpotential becomes
WIII = WMSSM + bHu(cWMYN minusr
3
10bBMYB)bL+ bHu
bXMYXbDc
+1
2bBMMB
bBM +1
2bGMMG
bGM +1
2cWMMW
cWM + bXMMXbXM
giving
mν = minusv2u
2
bdquo
3
10Y T
B Mminus1B YB +
1
2Y T
WMminus1W YW
laquo
≃ minusv2u4
10Y T
WMminus1W YW
last step valid if MB ≃ MW and YB ≃ YW
rArr Casas-Ibarra decomposition for YW as in type-I up to factor 45
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 15
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
M1M
2M
3 (
Ge
V)
MSeesaw (GeV)
M1
M2
M3
0
500
1000
1500
2000
2500
1012
1013
1014
1015
1016
|MQ
||M
L||M
E| (G
eV
)MSeesaw (GeV)
|ME|
|ML|
|MQ|
750
1000
1250
1500
1750
2000
2250
1012
1013
1014
1015
1016
Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2The SU(5)-broken phase
Under SU(3) times SUL(2) times U(1)Y
The 5 10 and 5H contain
5M = ( bDc bL) 10 = (bUc bEc bQ) 5H = ( bHc bHu) 5H = ( bHc bHd)
The 15 decomposes as
15 =bS(6 1minus2
3) + bT (1 3 1) + bZ(3 2
1
6)
The 24 decomposes as
24M =cWM (1 3 0) + bBM (1 1 0) + bXM (3 2minus5
6)
+ bXM (3 25
6) + bGM (8 1 0)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 12
ΦTP2Seesaw I
Postulate very heavy right-handed neutrinos yielding the following superpotential below
MGUT
WI =WMSSM +Wν
Wν = bNcYνbL middot bHu +
1
2bNcMR
bNc
Neutrino mass matrix
mν = minusv2u
2Y T
ν Mminus1R Yν
Inverting the seesaw equation gives Yν a la Casas amp Ibarra
Yν =radic
2i
vu
q
MR middotR middotp
mν middot Udagger
mν MR diagonal matrices containing the corresponding eigenvalues
U neutrino mixing matrix
R complex orthogonal matrix
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 13
ΦTP2Seesaw II
Below MGUT the superpotential reads
WII = WMSSM +1radic2(YT
bL bT1bL+ YS
bDcbS1
bDc) + YZbDc
bZ1bL
+1radic2(λ1
bHdbT1
bHd + λ2bHu
bT2bHu) +MT
bT1bT2 +MZ
bZ1bZ2 +MS
bS1bS2
fields with index 1 (2) originate from the 15-plet (15-plet)
The effective mass matrix is
mν = minusv2u
2
λ2
MTYT
Note that
YT = UT middot YT middot U
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 14
ΦTP2Seesaw III
In the SU(5) broken phase the superpotential becomes
WIII = WMSSM + bHu(cWMYN minusr
3
10bBMYB)bL+ bHu
bXMYXbDc
+1
2bBMMB
bBM +1
2bGMMG
bGM +1
2cWMMW
cWM + bXMMXbXM
giving
mν = minusv2u
2
bdquo
3
10Y T
B Mminus1B YB +
1
2Y T
WMminus1W YW
laquo
≃ minusv2u4
10Y T
WMminus1W YW
last step valid if MB ≃ MW and YB ≃ YW
rArr Casas-Ibarra decomposition for YW as in type-I up to factor 45
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 15
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
M1M
2M
3 (
Ge
V)
MSeesaw (GeV)
M1
M2
M3
0
500
1000
1500
2000
2500
1012
1013
1014
1015
1016
|MQ
||M
L||M
E| (G
eV
)MSeesaw (GeV)
|ME|
|ML|
|MQ|
750
1000
1250
1500
1750
2000
2250
1012
1013
1014
1015
1016
Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Seesaw I
Postulate very heavy right-handed neutrinos yielding the following superpotential below
MGUT
WI =WMSSM +Wν
Wν = bNcYνbL middot bHu +
1
2bNcMR
bNc
Neutrino mass matrix
mν = minusv2u
2Y T
ν Mminus1R Yν
Inverting the seesaw equation gives Yν a la Casas amp Ibarra
Yν =radic
2i
vu
q
MR middotR middotp
mν middot Udagger
mν MR diagonal matrices containing the corresponding eigenvalues
U neutrino mixing matrix
R complex orthogonal matrix
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 13
ΦTP2Seesaw II
Below MGUT the superpotential reads
WII = WMSSM +1radic2(YT
bL bT1bL+ YS
bDcbS1
bDc) + YZbDc
bZ1bL
+1radic2(λ1
bHdbT1
bHd + λ2bHu
bT2bHu) +MT
bT1bT2 +MZ
bZ1bZ2 +MS
bS1bS2
fields with index 1 (2) originate from the 15-plet (15-plet)
The effective mass matrix is
mν = minusv2u
2
λ2
MTYT
Note that
YT = UT middot YT middot U
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 14
ΦTP2Seesaw III
In the SU(5) broken phase the superpotential becomes
WIII = WMSSM + bHu(cWMYN minusr
3
10bBMYB)bL+ bHu
bXMYXbDc
+1
2bBMMB
bBM +1
2bGMMG
bGM +1
2cWMMW
cWM + bXMMXbXM
giving
mν = minusv2u
2
bdquo
3
10Y T
B Mminus1B YB +
1
2Y T
WMminus1W YW
laquo
≃ minusv2u4
10Y T
WMminus1W YW
last step valid if MB ≃ MW and YB ≃ YW
rArr Casas-Ibarra decomposition for YW as in type-I up to factor 45
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 15
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
M1M
2M
3 (
Ge
V)
MSeesaw (GeV)
M1
M2
M3
0
500
1000
1500
2000
2500
1012
1013
1014
1015
1016
|MQ
||M
L||M
E| (G
eV
)MSeesaw (GeV)
|ME|
|ML|
|MQ|
750
1000
1250
1500
1750
2000
2250
1012
1013
1014
1015
1016
Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Seesaw II
Below MGUT the superpotential reads
WII = WMSSM +1radic2(YT
bL bT1bL+ YS
bDcbS1
bDc) + YZbDc
bZ1bL
+1radic2(λ1
bHdbT1
bHd + λ2bHu
bT2bHu) +MT
bT1bT2 +MZ
bZ1bZ2 +MS
bS1bS2
fields with index 1 (2) originate from the 15-plet (15-plet)
The effective mass matrix is
mν = minusv2u
2
λ2
MTYT
Note that
YT = UT middot YT middot U
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 14
ΦTP2Seesaw III
In the SU(5) broken phase the superpotential becomes
WIII = WMSSM + bHu(cWMYN minusr
3
10bBMYB)bL+ bHu
bXMYXbDc
+1
2bBMMB
bBM +1
2bGMMG
bGM +1
2cWMMW
cWM + bXMMXbXM
giving
mν = minusv2u
2
bdquo
3
10Y T
B Mminus1B YB +
1
2Y T
WMminus1W YW
laquo
≃ minusv2u4
10Y T
WMminus1W YW
last step valid if MB ≃ MW and YB ≃ YW
rArr Casas-Ibarra decomposition for YW as in type-I up to factor 45
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 15
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
M1M
2M
3 (
Ge
V)
MSeesaw (GeV)
M1
M2
M3
0
500
1000
1500
2000
2500
1012
1013
1014
1015
1016
|MQ
||M
L||M
E| (G
eV
)MSeesaw (GeV)
|ME|
|ML|
|MQ|
750
1000
1250
1500
1750
2000
2250
1012
1013
1014
1015
1016
Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Seesaw III
In the SU(5) broken phase the superpotential becomes
WIII = WMSSM + bHu(cWMYN minusr
3
10bBMYB)bL+ bHu
bXMYXbDc
+1
2bBMMB
bBM +1
2bGMMG
bGM +1
2cWMMW
cWM + bXMMXbXM
giving
mν = minusv2u
2
bdquo
3
10Y T
B Mminus1B YB +
1
2Y T
WMminus1W YW
laquo
≃ minusv2u4
10Y T
WMminus1W YW
last step valid if MB ≃ MW and YB ≃ YW
rArr Casas-Ibarra decomposition for YW as in type-I up to factor 45
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 15
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
M1M
2M
3 (
Ge
V)
MSeesaw (GeV)
M1
M2
M3
0
500
1000
1500
2000
2500
1012
1013
1014
1015
1016
|MQ
||M
L||M
E| (G
eV
)MSeesaw (GeV)
|ME|
|ML|
|MQ|
750
1000
1250
1500
1750
2000
2250
1012
1013
1014
1015
1016
Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
M1M
2M
3 (
Ge
V)
MSeesaw (GeV)
M1
M2
M3
0
500
1000
1500
2000
2500
1012
1013
1014
1015
1016
|MQ
||M
L||M
E| (G
eV
)MSeesaw (GeV)
|ME|
|ML|
|MQ|
750
1000
1250
1500
1750
2000
2250
1012
1013
1014
1015
1016
Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Effect of heavy particles on MSSM parameters
MSSM (b1 b2 b3) = (335 1minus3)
per 15-plet ∆bi = 72 rArr type II model ∆bi = 7
per 24-plet ∆bi = 5 rArr type III model ∆bi = 15
M1M
2M
3 (
Ge
V)
MSeesaw (GeV)
M1
M2
M3
0
500
1000
1500
2000
2500
1012
1013
1014
1015
1016
|MQ
||M
L||M
E| (G
eV
)MSeesaw (GeV)
|ME|
|ML|
|MQ|
750
1000
1250
1500
1750
2000
2250
1012
1013
1014
1015
1016
Q = 1 TeV m0 = M12 = 1 TeV A0 = 0 tanβ = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 16
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Effect on heavy particles on MSSM spectrum IM
h
mχ
0 1
mχ
+ 1 (
Ge
V)
MSeesaw (GeV)
Mh
mχ01
mχ+1
0
200
400
600
800
1000
1012
1013
1014
1015
1016
MA
mχ
0 2
mχ
+ 2 (
Ge
V)
MSeesaw (GeV)
MA
mχ02
mχ+2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1012
1013
1014
1015
1016
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
Full lines seesaw type I dashed lines type II dash-dotted lines type III
degenerate spectrum of the seesaw particles
J N Esteves M Hirsch WP J C Romao F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 17
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2rdquoInvariantsrdquo
1012
1013
1014
1015
1016
15
2
3
1 10(m
2 Qminus
m2 E)
M2 1
1 10(m
2 Dminus
m2 L)
M2 1
(m2 Lminus
m2 E)
M2 1
(m2 Qminus
m2 U)
M2 1
M15 = M24 [GeV]
Seesaw I (≃ MSSM)
m2
Qminusm2
E
M2
1
≃ 20m2
Dminusm2
L
M2
1
≃ 18
m2
Lminusm2
E
M2
1
≃ 16m2
Qminusm2
U
M2
1
≃ 155
(solution of 1-loop RGEs)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
J Esteves MHirsch J Romatildeo W P F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 18
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2rdquoInvariantsrdquo limits for seesaw type-III models
1013
1014
1015
1016
1
15
2
25
3
35
4
(m2 Lminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
1013
1014
1015
1016
1
2
3
4
5
1 10(m
2 Qminus
m2 E)
M2 1
M24 [GeV]
SPS3m0 = 05 M12 = 1 TeVm0 = 1 M12 = 1 TeV
blue lines SPS3
light blue lines m0 = 500 GeV and M12 = 1 TeV
red lines m0 = M12 = 1 TeV
black line analytical approximation
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 19
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2LFV in the slepton sector approximate formulas I
one-step integration of the RGEs assuming mSUGRA boundary
∆M2Lij ≃ minus ak
8π2
`
3m20 + A2
0
acute
ldquo
Y kdaggerN LY k
N
rdquo
ij
∆Alij ≃ minus ak3
16π2A0
ldquo
YeYkdaggerN LY k
N
rdquo
ij
∆M2Eij ≃ 0
Lij = ln(MGUT Mi)δij
for i 6= j with Ye diagonal
aI = 1 aII = 6 and aIII =9
5
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 20
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2LFV in the slepton sector approximate formulas II
(∆M2L)ij and (∆Al)ij induce
lj rarr liγ lil+k l
minusr
lj rarr liχ0s
χ0s rarr li lk
Neglecting L-R mixing
Br(li rarr ljγ) prop α3m5li
|(δm2L)ij |2
em8tan2 β
Br(τ2 rarr e+ χ01)
Br(τ2 rarr micro+ χ01)
≃ldquo (∆M2
L)13
(∆M2L)23
rdquo2
Moreover in most of the parameter space
Br(li rarr 3lj)
Br(li rarr lj + γ)≃ α
3π
ldquo
log(m2
li
m2lj
) minus 11
4
rdquo
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 21
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Seesaw I
take all parameters real
U = UTBM =
0
B
B
B
q
23
1radic3
0
minus 1radic6
1radic3
1radic2
1radic6
minus 1radic3
1radic2
1
C
C
C
A
R =
0
B
B
1 0 0
0 1 0
0 0 1
1
C
C
A
Use 2-loop RGEs and 1-loop corrections including flavour effects
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 22
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Seesaw I
(GeV)1M
1010 1210 1410
1610
)j
3 l
rarr i)B
r(l
γ j
lrarr i
Br(l
-1810
-1710
-1610
-1510
-1410
-1310
-1210
-1110
-1010
-910
-810
-710
-610
)micro 3 rarrτBr( 3 e )rarrmicroBr( 3 e )rarrτBr(
)γ micro rarrτBr()γ e rarrmicroBr()γ e rarrτBr(
=0 eV1
νm
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 23
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Seesaw I
(GeV)1M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
(GeV)2M
1010 1110 1210
1310 1410
1510
1610
)χ
micro rarr
τsim) B
r(
χ e
rarr
τsimB
r(
-610
-510
-410
-310
-210
-110
1
)χ e rarr τsimBr(
)χ micro rarr τsimBr(
Excluded by
)γ e rarr microBr(
=0 eV1
νm
degenerate νR hierarchical νR
(M1 = M3 = 1010 GeV)
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch et al Phys Rev D 78 (2008) 013006
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 24
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Seesaw I
Texture models hierarchical νR
real textures rdquocomplexificationrdquo of one texture
SPS1arsquo (M0 = 70 GeV M12 = 250 GeV A0 = minus300 GeV tan β = 10 micro gt 0)
F Deppisch F Plentinger G Seidl JHEP 1101 (2011) 004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 25
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Seesaw II with a pair of 15-plets
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
10-4
10-6
10-8
10-10
10-12
10-14
10-16
Br H
li
reglj ΓL
BrH Τ reg ΜΓL
BrH Μ reg eΓL
BrH Τ reg eΓL
1011 1012 1013 1014 1015 1016
M15 = MTGeVD
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
Br H
Τ
2reg
Χ1
eL
Br H
Τ
2reg
Χ1
ΜL
BrH Τ2 reg Χ1 eL
BrH Τ2 reg Χ1 ΜL
Excluded by
BrH Μ reg eΓL
λ1 = λ2 = 05
SPS3 (M0 = 90 GeV M12 = 400 GeV A0 = 0 GeV tan β = 10 micro gt 0)
M Hirsch S Kaneko W P Phys Rev D 78 (2008) 093004
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 26
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Seesaw III in comparisonB
r(micro
rarr e
γ)
MSeesaw (GeV)
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-18
10-16
10-14
10-12
10-10
10-8
1010
1011
1012
1013
1014
1015
1016
III
II
I Br(
micro rarr
e γ
)
s213
m0=M12=1000 (GeV) tanβ=10 A0=0 (GeV)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-4
10-3
10-2
10-1
III δDirac = 0
III δDirac = π
I δDirac = 0
I δDirac = π
degenerate spectrum of the seesaw particles Mseesaw = 1014 GeV
J Esteves MHirsch J Romatildeo WP F Staub Phys Rev D83 (2011) 013003
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 27
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Masses at LHC
~q lnear ~01q~02 ~lR lfar0
500
1000
1500
0 20 40 60 80 100
m(ll) (GeV)
Eve
nts
1 G
eV1
00 fb
-1
G Polesello
5 kinematical observables depending on 4 SUSY masses
eg m(ll) = 7702 plusmn 005 plusmn 008
rArr mass determination within 2-5
For background suppression
N(e+eminus) +N(micro+microminus) minusN(e+microminus) minusN(micro+eminus)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 28
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Seesaw I + II signal at LHC
200 400 600 800
M12
[GeV]
10-5
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
400 600 800
M12
[GeV]
10-4
10-3
10-2
10-1
100
101
σ(χ
20) times
BR
[fb
]
m0=100 GeV
m0=200 GeV
m0=300 GeV
m0=500 GeV
σ(pprarr χ02) timesBR(χ0
2 rarr P
ij lilj rarr microplusmnτ∓χ01)
A0 = 0 tan β = 10 micro gt 0 (Seesaw II λ1 = 002 λ2 = 05)
JN Esteves et al JHEP 0905 003 (2009)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 29
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Low scale Seesaw
general problem up to now mν ≃ 01 eV rArr Y 2M fixed
However dim-5 operator might be forbidden due to symmetries
eg Z3 + NMSSMdagger
(LHu)2S
M26
(LHu)2S2
M37
solves at the same time the micro-problem
WMSSM = HdLYeEC + HdQYdD
C + HuQYuUC minus λHdHuS +
κ
3S3
flavour symmetries + extra SU(2) doublets + singletts
or linear or inverse seesaw rArr see talk by M Krauss
dagger I Gogoladze N Okada Q Shafi PLB 672 (2009) 235
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 30
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2NMSSM phenomenology in a nut-shell
Higgs sector h0i (i=123) a0
i (i=12)
non-standard Higgs decayslowast
h0i rarr a0
1a01 rarr 4b 2bτ+τminus τ+τminusτ+τminus
Neutralinos Singlino LSP |λ| ≪ 1 rArr displaced vertexdagger eg
Γ(τ1 rarr χ01τ) prop λ2
r
m2τ1
minusm2χ0
1
minusm2τ
Note micro = λvs
lowast see eg U Ellwanger J F Gunion and C Hugonie JHEP 0507 (2005) 041
dagger see eg U Ellwanger and C Hugonie Eur Phys J C 5 (1998) 723
S Hesselbach F Franke and H Fraas Phys Lett B 492 (2000) 140
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 31
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2arbitrary M 2Eij M 2
Lij Alij χ02 rarr lilj rarr lkljχ
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
1middot 10-12 1middot 10-10 1middot 10-8
00001
0001
001
01
BR(χ02 rarr χ0
1 eplusmn τ∓)
BR(τ rarr eγ)
BR(χ02 rarr χ0
1 microplusmn τ∓)
BR(τ rarr microγ)
Variations around SPS1a(M0 = 100 GeV M12 = 250 GeV A0 = minus100 GeV tan β = 10)
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 32
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Flavour mixing and edge variables
0 20 40 60 800
002
004
006
008
100Γtot
dΓ(χ02rarrlplusmni l
∓j χ
01)
dm(lplusmni l∓j )
eplusmnτ∓
microplusmnτ∓
eplusmnmicro∓
m(lplusmni l∓j ) [GeV]0 20 40 60 80
0
001
002
003
004
005
100Γtot
dΓ(χ02rarrl+lminusχ0
1)dm(l+lminus)
e+eminus(= micro+microminus) [LFC]
micro+microminus
e+eminus
m(l+lminus) [GeV]
A Bartl et al Eur Phys J C 46 (2006) 783
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 33
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Phases special cancelation regions
1024 de 108 BR(τ rarr eγ)
Variations around SPS3
see also A Bartl W Majerotto WP D Wyler PRD 68 (2003) 053005
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 34
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Squarks variations around SPS1arsquo
δDRR23
δLL23
δDLR32
δDLR23
27 middot 10minus4 le BR(b rarr sγ) le 43 middot 10minus4 135 psminus1 le |∆MBs| le 211 psminus1
δLLij =(M2
q LL)ij
m2
q
δqRRij =(M2
q RR)ij
m2
q
δqLRij =(M2
q LR)ij
m2
q
(i 6= j)
T Hurth WP JHEP 0908 (2009) 087
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 35
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Edge variables in the squark sector
x
x
200 300 400 500 600
0
01
02
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
tt
ct
x
x
100 300 500 700 900 1100
0
001
002
003
004
005
006
007
Mujuk[GeV]
100 dBr(g rarr ujukχ0
1)dMujuk
[GeVminus1]
ct
tt
mg = 800 GeV mujgtsim 560 GeV
δLLij = 006 δRRuij = 006
σ(pprarr gg) ≃ 2 pb
mg = 1300 GeV mu1= 470 GeV muj
gtsim 1 TeV
δLLij = 017 δRRuij = 061
σ(pprarr gg) ≃ 40 fb
A Bartl et al PLB 679 (2009) 260 PLB 698 (2011) 380
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 36
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Conclusions
MSSM extensions in view of neutrino physics
SUSY flavour problem orginates in the SM flavour problem
Dirac neutrinos displaced vertices if νR LSP eg t1 rarr lbνR (but NMSSM
t1 rarr lbνχ01)
Seesaw models
most promising τ2 decays
difficult to test at LHC signals of O(10 fb) or below
in case of seesaw II or III different mass ratios
NMSSM
potenitally larger LFV signals due to lower seesaw scale
modified Higgsneutralino sector
modified phenomenology h01 rarr a1a1 andor displace vertices
Squarks similar techniques for flavour violating signals as for sleptons but technically
more challanging
general MSSM larger effects require special parameter combinations
rArr hint of hidden symmetries
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 37
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Landau Poles
8 10 12 14 16
08
10
12
14
16
18
20
log(MSeesawGeV)
g GU
T
m0 = M12 = 1 TeV A0 = 0 tan β = 10 and micro gt 0
MGUT = 2 times 1016 GeV
black lines seesaw type-II
green lines seesaw type-III with three 24-plets with degenerate mass spectrum
full (dashed) lines 2-loop (1-loop) results
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 38
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-
ΦTP2Seesaw special kinematicsdagger
mSugra stau co-annihilation for DM in particular mτ1 minus mχ01
ltsim
mτ
τ1
(a)
χ01
τ
(b)
χ01
τ1
τ
π
ντ
χ01
ντ
νl
lW
τ
τ1
(c)
(a)
lα
χ01
1Me 2
Rτ minusMe 2Rα
lαRτR ≃ l1
∆M 2 eRRατ
χ01
lα
(b)
1Me 2
Rτ minusMe 2Lα
M 2 eLRττ ∆M 2 e
LL ατ
lαLτLτR ≃ l1
1Me 2
Rτ minusMe 2Lτ
τ1 life times up to 104 sec
dagger S Kaneko et al Phys Rev D 78 (2008) 116013
FLASY 2011 20 July 2011 W Porod Uni Wurzburg ndash p 39
- small hspace 2cm Overview
- small hspace 2cm Supersymmetry MSSM
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Flavour Generalities
- small hspace 2cm Lepton flavour violation experimental data
- small hspace 2cm Dirac neutrinos MFV scenario
- small hspace 2cm Dirac neutrinos NLSP life times
- small hspace 2cm Majorana neutrinos Seesaw mechanism$^$
- small hspace 2cm The Setup GUT scale
- small hspace 2cm The $SU(5)$-broken phase
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II
- small hspace 2cm Seesaw III
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect of heavy particles on MSSM parameters
-
- small hspace 2cm Effect on heavy particles on MSSM spectrum I
- small hspace 2cm Invariants
- small hspace 2cm Invariants limits for seesaw type-III models
- small hspace 2cm LFV in the slepton sector approximate formulas I
- small hspace 2cm LFV in the slepton sector approximate formulas II
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw I
- small hspace 2cm Seesaw II with a pair of $15$-plets
- small hspace 2cm Seesaw III in comparison
- small hspace 2cm Masses at LHC
- small hspace 2cm Seesaw I + II signal at LHC
- small hspace 2cm small Low scale Seesaw
- small hspace 2cm small NMSSM phenomenology in a nut-shell
- small hspace 2cm small arbitrary $M^2_Eij$ $M^2_Lij$ $A_lij$ $ilde chi ^0_2 o ilde l_i l_j o l_k l_j ilde chi ^0_1 $
- small hspace 2cm small Flavour mixing and edge variables
- small hspace 2cm Phases special cancelation regions
- small hspace 2cm Squarks variations around SPS1a
- small hspace 2cm Edge variables in the squark sector
- small hspace 2cm small Conclusions
- small hspace 2cm Landau Poles
- small hspace 2cm small Seesaw special kinematics$^dagger $
-